This also relates to problem with installing to MBR and there is no room
for embedding core.img there. I have been using USB stick where there is
not enough room for core.img what I want to store there. So only option
is to leave core.img to filesystem and install MBR.

But then you can add an empty partition (type 0x00) starting at sector 63,
and grub-setup will overwrite it.
Or you could leave that region unpartitioned.

At least on my disks there is 32 KiB free space. But not ~50 KiB what my
core.img requires.